Arthur, we keep hearing that momentum and KE are related but not the same thing, I even said so in one of my earlier posts on this topic. I think we should define them both and explain the difference.

Kinetic Energy: the mechanical energy that a body has by virtue of its motion

Momentum: a property of a moving body that determines the length of time required to bring it to rest when under the action of a constant force

These are both definitions straight out of webster's dictionary. So, as you can see, KE is the energy it contains, and momentum is how long it will stay in motion by virtue of it's mass. I bring back the rock example. I can throw a pepple not very far at all, but I can throw it fast. But, because it is so light, it has no momentum (nothing behind it to keep it moving). I can throw a rock farther because of it's weight, but I can't throw a boulder at all.
Same is true with arrows. A light arrow may produce more initial KE because of its speed,but by 30 yards it has slowed down so much that the KE drops off quickly; momentum. A heavier arrow may or may not have the same initial KE because of it's slower speed, but it retains its speed longer downrange (momentum) thus retaining it's KE.
Let's say a 300 gr. arrow (I'm making these numbers up, but the concept is actual) is flying at 310 fps producing KE of 64#, but remember, that's at the point of release. By 30 yards let's say it's speed has decelerated to 260 fps, so the KE at 30 yards is 45#, a drastic decrease.
Now let's shoot a 450 gr. arrow. It's launch speed may only be 260 fps, giving a KE of 68#. Now, at 30 yards downrange it's speed is 240 fps (yes, the arrow has dropped more than the lighter one, but that's because of gravity, not speed, it's speed, by virtue of it's momentum has not dropped off so much) giving a KE of 58#.

So, yes, momentum and KE are both measured by velocity and mass, but they are not the same thing.



All numbers here, again, were fictional, (with the exception of the math) but I believe them to be fair and at least close.